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Irving Fisher —Mathematical investigations

the other two) it is only necessary to have a plane curve of appro-priate form and to represent any two of the above economic magni-tudes by any two geometrical magnitudes determined by the posi-tion of points in the curve.

Out of the numerous possible methods thus included, the one se-lected for the preceding discussion was to represent marginal utilityby the Cartesian ordinate and commodity by the area included be-tween the curve, the axes of coordinates, and the abscissa drawnfrom the point.

§ 2 .

In order to show the connection between this system of coordi-nates and those of Jevons and of Auspitz und Lieben, the followingscheme is presented :

Commodity

Jeyons .

.... = Xj

Auspitz & Lieben. The new curves.

= = fxdy

Marginal )utility f

---- = Vi

_ dy a __ tan ^ — ydx a y

Total [

utility \

- fl/jd-Xj

= y« - fyxdy

Gain.

---- —

= V a-^ —fyxdy-yfxdy

29 . 30 .